How do you use the definition of a derivative to find the derivative of $f (x) = 3 x + 2$ $f(x)=3x+2$ ?

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Answer 1 · 2016-12-07T18:01:27

$f'(x)=(df)/(dx)=3$
(see below for method using the definition of a derivative).

The definition of the derivative of $f(x)$ is
$color(white)("XXX")f'(x)=(df)/(dx)= lim_(hrarr0) (f(x+h)-f(x))/h$

For the example $f(x)=3x+2$
$color(white)("XXX")(df)/(dx)= lim_(hrarr0) ((3(x+h)+2)-(3x+2))/h$

$color(white)("XXXXX")=lim_(hrar0) (cancel(3x)+3hcancel(+2)cancel(-3x)cancel(-2))/h$

$color(white)("XXXXXX")=lim_(harrr0) (3cancel(h))/cancel(h)$

$color(white)("XXXXXX")=lim_(hrarr0) 3$

$color(white)("XXXXXX")=3$

How do you use the definition of a derivative to find the derivative of f(x)=3x+2f(x)=3x+2f(x)=3x+2?